In this paper we investigate the problem of optimising the speed of a vehicle over a fixed path for minimum time traversal. We utilise a change of variables that has been known since the 1980s, although the resulting convexity of the problem was not noted until recently. The contributions of this paper are three fold. First, we extend the convexification of the problem to a more general framewo...

We give a complete characterization of constant quadratic functions over an affine variety. This result is used to convexify the objective function of a general quadratic programming problem (Pb) which contains linear equality constraints. Thanks to this convexification, we show that one can express as a semidefinite program the dual of the partial Lagrangian relaxation of (Pb) where the linear...

In this paper we investigate the problem of optimizing the speed of a vehicle over a fixed path for minimum time traversal. We utilize a change of variables that has been known since the 1980s, although the resulting convexity of the problem was not noted until recently. The contributions of this paper are three fold. First, we extend the convexification of the problem to a more general framewo...

In this paper, an algorithm is introduced to find an optimal solution for an optimization problem that arises in total least squares with inequality constraints, and in the correction of infeasible linear systems of inequalities. The stated problem is a nonconvex program with a special structure that allows the use of a reformulation–linearization–convexification technique for its solution. A b...

Mean field type differential inclusions appear within the theory of mean control through convexification a right-hand side. We study case when side inclusion depends on state an agent and distribution agents in upper semicontinuous way. The main result paper is existence stability solution inclusion. Furthermore, we show that value function optimal problem initial parameter semicontinuously.

This paper is concerned with the inverse scattering problem which aims to determine spatially distributed dielectric constant coefficient of 2D Helmholtz equation from multifrequency backscatter data associated a single direction incident plane wave. We propose globally convergent convexification numerical algorithm solve this nonlinear and ill-posed problem. The key advantage our method over c...

This letter presents a novel optimization framework of formulating the three-phase optimal power flow that involves uncertainty. The proposed uncertainty-aware (UaO) is: 1) deterministic is less complex than existing frameworks involving uncertainty, and 2) convex such it admits polynomial-time algorithms mature distributed methods. To construct this UaO framework, methodology learning-aided mo...

We consider an energy minimization problem for a two-component composite with fixed volume fractions. We study two questions. The first is the dependence of the minimum energy on the constraints and parameters. The second is the rigorous justification of the method of Lagrange multipliers for this problem. We are able to treat only cases with periodic or affine boundary condition. We show that ...

In this contribution we address the efficient solution of optimal control problems of dynamic processes with many controls. Such problems typically arise from the convexification of integer control decisions. We treat this problem class using the direct multiple shooting method to discretize the optimal control problem. The resulting nonlinear problems are solved using an SQP method. Concerning...